> the calculation is straightforward

Ok then, make it easy - your requirement is to independently pick 4 numbers from the range 0 to 9, without resulting in any duplicates. Which is more likely to be successful:

- pick 4 random digits independently

- pick a random digit, which will be appended by the next digit as pick #2 (i.e. if you pick 5, then 6 will automatically be your second digit, if you pick 9, 0 will be your second digit). Then pick once more on the same terms.

The math here is easy: scenario 1 you have 0.9 x 0.8 x 0.7 = 0.504 likelihood of success. Scenario 2 it's simply 0.7.